# 4) Error Correction

#### Florian Berding and Julia Pargmann

#### 2025-07-18

# 1 Introduction

Literature regarding content analysis often presents the estimation of reliability as a part of the development phase of a coding scheme, for example to inform a revision (Krippendorff, 2019; Kuckartz, 2018; Mayring, 2015; Schreier, 2012). If the reliability is considered to be sufficient, the main study starts. Often, the reliability of the codings of this main study is not further controlled, as it is assumed that the reliability estimates of the development phase hold for the entire main study. Sometimes however, researchers communicate and discuss their findings and assign a category to a coding unit by agreeing on the relevant category when the coding scheme is unclear.

With Iota Concept, the reliability of a coding scheme can be taken into account more explicitly during the main study. It provides the opportunity for error corrections, which is not possible with traditional measures such as Percentage Agreement, Cohen’s Kappa or Krippendorff’s Alpha.

The error correction of the Iota Concept is based on two ideas. First, an Assignment Error Matrix produces patterns of ratings for every coding unit. These patterns give hints which true category may be the source for this kind of observation. This requires at least two raters. Second, involving additional raters provides more information on a coding unit, which can improve the assignments. This idea is similar to the application of multiple items in questionnaires or tests where each item can be considered as a test for the phenomena of interest. Additional test are used to reduce errors.

In this vignette, we would like to continue our example of the exams from the first vignette and now want to show you how the error correction can be applied.

# 2 Using the error correction of the Iota Concept

Applying the error correction of the Iota Concept requires that all coding units of the core study are rated by at least two raters. The error correction can be requested with the function `est_expected_categories()`. This function calculates the probability that a coding unit belongs to a specific true category under the condition of the observed pattern. To illustrate the error correction, a look into the data set is helpful.

    library(iotarelr)
    head(iotarelr_written_exams)
    #>   Coder A Coder B Coder C    Sex
    #> 1 average average    good female
    #> 2 average    poor average   male
    #> 3    poor average    poor female
    #> 4 average average average female
    #> 5    poor average    good female
    #> 6    poor    poor average female

The first 6 rows of the data set show that the three raters do not agree on all coding units. While the raters agree on the first two exams, they disagree partially on exams 3 to 6. In particular, two raters consider exam 3 to be average while one rater considers this exams to be good. Thus, there seems to be some kind of error and it is not clear which category should be assigned to exam 3.

To solve this problem, we must first estimate the Assignment Error Matrix. In the next step, we pass the estimated Assignment Error Matrix to the function `est_expected_categories()` and use the ratings as our data source. The results are saved in the object `expected_categories`.

    res_iota2<-compute_iota2(
      data=iotarelr_written_exams[c("Coder A","Coder B","Coder C")],
      random_starts = 10,
      trace = FALSE)
    expected_categories<-est_expected_categories(
      data=iotarelr_written_exams[c("Coder A","Coder B","Coder C")],
      aem=res_iota2$categorical_level$raw_estimates$assignment_error_matrix)
    head(expected_categories)
    #>   Coder A Coder B Coder C prob_average  prob_good  prob_poor expected_category
    #> 1 average average    good 4.843038e-01 0.36354973 0.15214649           average
    #> 2 average    poor average 1.577095e-07 0.27608029 0.72391955              poor
    #> 3    poor average    poor 1.889099e-15 0.12917436 0.87082564              poor
    #> 4 average average average 9.169907e-01 0.04109588 0.04191343           average
    #> 5    poor average    good 1.642820e-08 0.48170371 0.51829628              poor
    #> 6    poor    poor average 1.889099e-15 0.12917436 0.87082564              poor

The resulting object contains the ratings and additional columns. The columns contain the probability that a coding unit belongs to a specific true category. The most plausible category is always presented in the last column.

For the first row, the probability that this exam is truly an average one is about 48.4%. The chance that this exam represents truly a good exam is about 36.3% and that is is truly a poor exam is about 15.2%. Thus, it is most plausible to assign exam number 1 to the category “average”.

For exam number two, the probability that this exam is truly an average one is about 0.00%. The chance that this exam represents truly a good exam is about 27.6% and that is is truly a poor exam is about 72.4%. Thus, it is most plausible to assign exam number 2 to the category “poor”.

If the ratings were done by only one rater, these kind of errors would not become visible. For example, if the exams were rated only by rater A, exam 2 would have been assigned as an average exam, although it is more plausible to assign it to the category “poor”.

# 3 Conclusions

Estimating the category that is most likely true has several advantages:

- It allows multiple testing of coding units by more than two raters.
- The additional information can be used to calculate the certainty of an assignment.
- The category that is most likely true is assigned to a coding unit.
- Errors made by only one rater can be avoided.
- Researchers do not need to discuss every coding unit, which binds financial and time resources for large sample sizes.

# References

- Früh, W. (2017). Inhaltsanalyse: Theorie und Praxis (9., überarbeitete Auflage). UTB.
- Krippendorff, K. (2019). Content Analysis: An Introduction to Its Methodology (4th Ed.). SAGE.
- Kuckartz, U. (2018). Qualitative Inhaltsanalyse: Methoden, Praxis, Computerunterstützung (4. Auflage). Grundlagentexte Methoden. Beltz.
- Mayring, P. (2015). Qualitative Inhaltsanalyse: Grundlagen und Techniken (12., überarbeitete Auflage). Beltz.
- Schreier, M. (2012). Qualitative Content Analysis in Practice. SAGE.